Programa de Engenharia Nuclear, COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68509, CEP 21941-972, Rio de Janeiro, RJ, Brazil
Copyright © 2010 Nilson C. Roberty and Marcelo L. S. Rainha. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the problem of reconstruction of an unknown characteristic transient
thermal source inside a domain. By introducing the definition of an extended dirichlet-to-Neumann map in the time-space cylinder and the adoption of the anisotropic Sobolev-Hilbert
spaces, we can treat the problem with methods similar to those used in the analysis of the stationary
source reconstruction problem. Further, the finite difference scheme applied to the
transient heat conduction equation leads to a model based on a sequence of modified Helmholtz
equation solutions. For each modified Helmholtz equation the characteristic star-shape source
function may be reconstructed uniquely from the Cauchy boundary data. Using representation
formula, we establish reciprocity functional mapping functions that are solutions of the modified
Helmholtz equation to their integral in the unknown characteristic support.